How to keep apps (that aren't in your iTunes) After updating software on iPhone?

My friend has recently given me his old iPhone 3GS with about 70+ apps all ready on it, all of them awesome. However, I can't download new apps (such as whatsapp, which is essential) and can't get imessage due to the outdated software. I have tried using imtoo iphone back up but whenever I try to put an app on my iPhone that's been ripped from it it says there's a problem with authorisation, presumably because I need authorisation from my friends account (which he's now lost the password to:/). At the moment it seems like my only option is to jailbreak it, unless I can find some software to change the authorisation on these apps. Any suggestions?

You didn't specific you wanna update to what version and what version you use on your iPhone now.

You can do it using iTunes, but it'll ask you for password (from account which use for purchased these apps), in case you don't have password, so you can't copy the apps to the computer via iTunes but I know one software that can let you to copy the apps from iPhone to PC, it called iFunBox. But, it still same problem if you don't have the password, coz when you wanna install again the apps to your iPhone, password is required (if using iTunes, not sure iFunBox, coz last time I use iFunBox to install app, it working, the app installed on my iPhone but the app automatically closed by itself)

For another optional for updating the iPhone w/o changing any apps on your iPhone, you can try on Setting > General > Software Update.